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# Prove that cosecA+cotA=1/(cosecA-cotA) using the LHS of the identity?

provided that cosecA is not equal to cotA

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- ted sLv 79 years agoFavorite Answer
you have { LHS} 1 / sin A + cos A / sin A = [ 1+ cos A] / sin A =

sin² A / { sin A [ 1 - cos A ] }= sin A / [ 1 - cos A ] = 1 / [ 1/sin A - cos A / sin A] =result

- G-boy S.S.Lv 69 years ago
LHS: cosec A + cot A

= ( 1 / sin A ) + ( cos A / sin A )

= ( 1 + cos A ) / sin A

.................................. multiply by [ ( 1 - cos A ) / sin A ] / [ ( 1 - cos A ) / sin A ]

= [ ( 1 - cos ² A ) / sin ² A ] / [ ( 1 - cos A ) / sin A ]

= ( sin ² A / sin ² A ) / [ ( 1 / sin A ) - ( cos A / sin A ) ]

= 1 / ( cosec A - cot A ) ............ b i n g o ! ! !

- sahsjingLv 79 years ago
cscA+cotA

= cscA (1+cosA)

= cscA(1-cos^2A)/(1-cosA)

= cscA sin^2A/(1-cosA)

= sinA/(1-cosA)

= 1/(cscA - cotA)

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